Maximal metric surfaces and the Sobolev-to-Lipschitz property

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak–Wenger, which satisfies a related maximality condition.

Modeling and calculation of hydromechanical systems dynamics based on the volume rigidity theory

A method for modeling hydraulic systems of hydromechanical devices based on the application of the volume rigidity theory - the property of the hydraulic system to keep its volume unchanged when the pressure of the working medium changes is proposed. The main analytical dependencies intended for modeling the hydraulic system are presented. An example of simulation and calculation of a hydromechanical shock absorber system which confirms the correctness and convenience of using the volume rigidity theory in modeling hydromechanical drive systems of complex machines is presented. The results of the numerical experiment make it possible to evaluate the functioning quality of the drive system under investigation to reveal the effect of the main design and system functional parameters on its operation. The graphs of the change in the main functional parameters of the shock absorber under investigation in real time are given, which make it possible to visually evaluate the results of a numerical experiment and draw conclusions about the need for modernization.

Projection of the hydraulic pressure drive with application of partial synthesis

In this article “Projection of a Hydraulic Pressure Drive with Application of Partial Synthesis” for the best comprehension and also receiving more complete picture, definitions of the term projection are considered, some fields of activity in which it is applied, namely technological, agricultural mechanical engineering etc are listed. An important part of cars, the drive is, the hydraulic actuator is most often applied – projection of which will be described in this article. First of all the existing technique projection of a hydraulic actuator is considered and its principle is described and shortcomings are designated. For carrying out a better designing process the new technique of projection of a hydraulic pressure drive which includes a stage of partial synthesis is offered. This stage allows explaining the theory of a volume rigidity which in turn allows to simplify calculations because it is possible to count several options of preliminary structures at the same time that will lead to receiving a hydraulic actuator with the best parameters, unlike the previous considered technique.